A system is described by its [[transition probability matrix]] (TPM), denoted <math>T_U = p(\mathbf{u}' \mid \mathbf{u})</math>, over all its possible states. From this, IIT defines:<ref name=":1" />
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''Intrinsic information'' (ii) for a state s over a possible cause/effect state <math>\tilde{s}</math>:
''Complexes'' are defined as the systems (subsets of units) that locally maximize φ. Their internal distinctions and relations form the Φ-structure of the system:
<math>\Phi</math> corresponds to the ''quantity'' of consciousness, while the particular structure of distinctions and relations defines its ''quality''.